fast and curious

Saturday Teaser Curio #73: A Family Shuffle

We’re celebrating immigrants this week here at Curious, so today’s Teaser has a refugee theme, which is appropriate since I am one. I came over as a baby with my family from Vietnam in 1975 (we left in a helicopter, though a boat makes for a much better Teaser below). When we arrived here, we were sponsored by an incredible family in Illinois. They showed us love, generosity, and how to make layer salad. All three were amazing! — Thai

A family of four refugees (mother, father, a boy, and a girl) come to a river they need to cross. There is an adult fisherman there who is willing to let them borrow his very small boat. The boat is large enough to carry one adult with no passengers or two kids (the kids know how to use the boat). What's the fewest number of times the boat needs to cross the river (either direction) to get the family across and leave the boat with the fisherman?

Note: The fisherman can be left on either side of the river, as long as he has his boat. No, they can't swim the river because... um... deadly snakes.

Ready for the answer?

There aren't any tricks here; you just have to start crossing the river, and always make sure there is a child available to take the boat back. Here's a way:

First, the children cross the river.

One child (say, the son) comes back.

The father crosses alone.

The other child (the daughter, in this case) comes back.

Then, both children cross the river again.

One child (say, the son) comes back.

The mother crosses alone.

The other child (the daughter) comes back.

Then, both children cross the river again.

One child (say, the son) comes back.

The fisherman crosses alone.

The other child (the daughter) comes back.

Finally, both children cross the river again.

At this point, all people are on the other side of the river, the family can leave and the fisherman has his boat. And the boat crossed the river 13 times.